paralleldomain.utilities.transformation¶

class Transformation(quaternion=None, translation=None)¶

Multi-purpose 6DoF object.

When printed, the rotation is given as euler angles in degrees following intrinsic rotation order XYZ, rounded to 2 decimal places.

Parameters

quaternion (Union[pyquaternion.quaternion.Quaternion, List[float], numpy.ndarray]) – Quaternion instance or elements for rotation. Elements are expected in order (w,x,y,z). Default: Unit quaternion without rotation.
translation (Union[numpy.ndarray, List]) – List-like translation information in order (x,y,z). Default: [0,0,0]

Example

Transformation instances can be easily matrix-multiplied with other Transformation instances or any np.ndarray of shape (4,n).

lidar_frame = ...  # get any `SensorFrame` from a LiDAR sensor
points_vehicle_frame = (lidar_frame.extrinsic @ lidar_frame.xyz_one.T).T
points_world_frame = (lidar_frame.pose @ lidar_frame.xyz_one.T).T

boxes_3d = lidar_frame.get_annotations(AnnotationTypes.BoundingBoxes3D)

for b in boxes_3d.boxes:
    box_pose_world_frame = lidar_frame.pose @ b.pose

property transformation_matrix: numpy.ndarray¶

Returns the homogeneous transformation matrix in shape (4,4).

/                  \
|R_11 R_12 R_13 t_x|
|R_21 R_22 R_23 t_y|
|R_31 R_32 R_33 t_z|
|0    0    0    1  |
\                  /

Return type: ndarray

property rotation: numpy.ndarray¶

Returns the rotation matrix in shape (3,3).

/              \
|R_11 R_12 R_13|
|R_21 R_22 R_23|
|R_31 R_32 R_33|
\              /

Return type: ndarray

property quaternion: pyquaternion.quaternion.Quaternion¶

Returns the rotation as a pyquaternion.quaternion.Quaternion instance.

Full documentation can be found in pyquaternion API Documentation.

To get the quaternion coefficients, either call .elements, iterate over the object itself or use the dedicated named properties. The element order (until explicitly stated otherwise) should always be assumed as (w,x,y,z) for function w + xi+ yj + zk

from paralleldomain.model.transformation import Transformation

tf = Transformation.from_euler_angles(yaw=90, pitch=0, roll=0, is_degrees=True)

assert(tf.quaternion.elements[0] == tf.quaternion[0] == tf.quaternion.w)
assert(tf.quaternion.elements[1] == tf.quaternion[1] == tf.quaternion.x)
assert(tf.quaternion.elements[2] == tf.quaternion[2] == tf.quaternion.y)
assert(tf.quaternion.elements[3] == tf.quaternion[3] == tf.quaternion.z)

Please note that when using scipy.spatial.transform.Rotation, scipy assumes the order as (x,y,w,z).

from paralleldomain.model.transformation import Transformation
from scipy.spatial.transform import Rotation
import numpy as np

tf = Transformation.from_euler_angles(yaw=90, pitch=0, roll=0, is_degrees=True)
tf_scipy = Rotation.from_quat([
    tf.quaternion.x,
    tf.quaternion.y,
    tf.quaternion.z,
    tf.quaternion.w
])

# Check that rotation quaternion is equal within tolerance
np.allclose(tf.rotation == tf_scipy.as_matrix())  # returns True

Return type: Quaternion

property translation: numpy.ndarray¶

Returns the translation vector (x,y,z) in shape (3,).

Return type: ndarray

property inverse: paralleldomain.utilities.transformation.Transformation¶

Returns the inverse transformation as a new Transformation object.

Return type: Transformation

classmethod from_transformation_matrix(mat)¶

Creates a Transformation object from an homogeneous transformation matrix of shape (4,4)

Parameters: mat (numpy.ndarray) – Transformation matrix as described in transformation_matrix
Returns: Instance of Transformation with provided parameters.
Return type: Transformation

as_euler_angles(order, degrees=False)¶

Returns the rotation of a Transformation object as euler angles.

Parameters

order (str) – Defines the axes rotation order. Use lower case for extrinsic rotation, upper case for intrinsic rotation. Ex: xyz, ZYX, xzx.
degrees (bool) – Defines if euler angles should be returned in degrees instead of radians. Default: False

Returns

Ordered array of euler angles with length 3.

Return type

ndarray

classmethod from_euler_angles(angles, order, translation=None, degrees=False)¶

Creates a transformation object from euler angles and optionally translation (default: (0,0,0))

Parameters

angles (Union[numpy.ndarray, List[float]]) – Ordered euler angles array with length 3
translation (Optional[numpy.ndarray]) – Translation vector in order (x,y,z). Default: [0,0,0]
order (str) – Defines the axes rotation order. Use lower case for extrinsic rotation, upper case for intrinsic rotation. Ex: xyz, ZYX, xzx.
degrees (bool) – Defines if euler angles are provided in degrees instead of radians. Default: False

Returns

Instance of Transformation with provided parameters.

Return type

Transformation